Exercise 8.2 class 10 maths | Class 10 Maths Exercise 8.2 | Trigonometry NCERT Solutions Explanation

Class 10 Maths Exercise 8.2 | Trigonometry NCERT Solutions | Full Explanation in Hindi 📚 Welcome to RAJAN SIR – your trusted channel for Class 10 Maths! In this video, we’ll cover Exercise 8.2 from Chapter 8: Trigonometry (NCERT) with detailed step-by-step solutions in simple Hindi. Perfect for CBSE 2025 Board Exam preparation! 🔔 Don’t forget to Like, Share & Subscribe for more exam-focused content. 📌 Topics Covered: Trigonometric identities Problem-solving tricks Board exam tips Time-saving methods #class10maths #trigonometry #exercise8_2 #ncertsolutions #cbse2025 #mathsbyrajansir #boardexam #class10tricks #trigonometryclass10 #mathsinHindi #class10term1 #mathswithrajansircbsetoppers Exercise 8.2 – Class 10 Maths NCERT (Chapter 8: Introduction to Trigonometry) Here are the NCERT solutions for Exercise 8.2 step-by-step: --- 🔷 Q1. Evaluate the following: (i) sin 60° cos 30° + sin 30° cos 60° We use: sin 60° = √3/2 cos 30° = √3/2 sin 30° = 1/2 cos 60° = 1/2 Solution: = (√3/2 × √3/2) + (1/2 × 1/2) = (3/4) + (1/4) = 1 --- (ii) 2tan 45° / (1 + tan² 45°) We know: tan 45° = 1 Solution: = 2 × 1 / (1 + 1²) = 2 / (1 + 1) = 1 --- (iii) sin²30° + cos²30° We know: sin 30° = 1/2 cos 30° = √3/2 Solution: = (1/2)² + (√3/2)² = 1/4 + 3/4 = 1 --- (iv) 2sin²60° + cos²45° - tan²30° Values: sin 60° = √3/2 cos 45° = 1/√2 tan 30° = 1/√3 Solution: = 2(3/4) + (1/√2)² - (1/√3)² = 3/2 + 1/2 - 1/3 = (3/2 + 1/2) - 1/3 = 2 - 1/3 = 5/3 --- 🔷 Q2. Evaluate: (i) (sin 30° + cos 30°)² + (sin 30° - cos 30°)² We use identity: (a + b)² + (a - b)² = 2(a² + b²) Let: sin 30° = 1/2 cos 30° = √3/2 Solution: = 2[(1/2)² + (√3/2)²] = 2[1/4 + 3/4] = 2 × 1 = 2 --- (ii) (2tan30°) / (1 + tan²30°) tan 30° = 1/√3 Solution: = 2 × (1/√3) / (1 + 1/3) = (2/√3) / (4/3) = (2/√3) × (3/4) = (6/4√3) = (3/2√3) Rationalizing: = (3√3) / (2×3) = √3/2 --- (iii) tanA × cotB + sinA × secB - cosA × cosecB Given: A = 30°, B = 60° Use: tan 30° = 1/√3, cot 60° = 1/√3 sin 30° = 1/2, sec 60° = 2 cos 30° = √3/2, cosec 60° = 2/√3 Solution: = (1/√3)(1/√3) + (1/2)(2) - (√3/2)(2/√3) = (1/3) + 1 - 1 = 1/3